The present invention relates to a method and system for encoding channels for digital communications. More specifically, this invention relates to the use of trellis codes designed for using intersymbol interference (ISI) to increase the reliability or reduce the complexity of high speed communication across bandlimited channels.
The practice of designing error control codes independently of channel considerations has a detrimental impact on the performance of systems, particularly of systems utilizing bandlimited channels. A solution to this problem known as trellis-coded modulation was described by Gottfried Ungerboeck in an article entitled "Channel Coding with Multilevel/Phase Signals," IEEE Transactions on Information Theory, Vol. IT-28, No. 1, pp. 55-67, January 1982. Ungerboeck incorporated a modulation scheme into the encoder, and relied on a heuristic partitioning technique. Channels with intersymbol interference (ISI), however, had to be equalized to remove the interference.
Attempts have been made to extend trellis-coded modulation to specific ISI channels. For example, in 1986, Wolf and Ungerboeck designed trellis codes for the binary partial response channel by partitioning the channel output by hand (J. K. Wolf and G. Ungerboeck, "Trellis Coding for Partial-Response Channels," IEEE Transactions on Communications, Vol. COM-34, No. 8, pp. 765-773, August 1986). They also showed that the same performance could be obtained using a convolutional code followed by a precoder for the channel. This latter approach gained support in 1989 when Forney and Calderbank argued that as the cardinality of the channel alphabet increases, the performance of the precoded partial response channel approaches that of the MLSE equalized channel (G. D. Forney, Jr. and M. V. Eyuboglu, "Combined Equalization and Coding Using Precoding" IEEE Communications Magazine, pp. 25-34, December 1991). This would seem to indicate that for the binary partial response channel, at least, the code design could be done independently of the channel. However, in 1994, Hole and Ytrehus concluded that for the binary 1-D channel, the best convolutional code to precede the precoder is not necessarily a maximum Hamming distance code. By designing the code to maximize the Euclidean distance at the output of the channel, it is often possible to improve the system performance (K. J. Hole and O. Ytrehus, "Improved Coding Techniques for Precoded Partial-Response Channels," IEEE Transactions on Information Theory, Vol. 40, No. 2, pp. 482-493, March 1994).
Another approach to code design for partial response channels has been disclosed by Forney, Calderbank, Karabed, Siegel wherein the codes utilized are matched spectral null codes (G. D. Forney, Jr., and A. R. Calderbank, in "Coset Codes for Partial Response Channels; Or, Coset Code in Spectral Nulls," IEEE Transactions on Information Theory, Vol. 35, No. 5, pp. 925-943, September 1989; R. Karabed and P. H. Siegel, "Matched Spectral-Null Codes for Partial-Response Channels," IEEE Transactions on Information Theory, Vol. 37, No. 3, pp. 818-855, May 1991). However in 1992, Haeb explored trellis code design by partitioning of the output of the q-ary partial response channel by exhaustive search, and concluded that this provided a generalization of the early matched spectral null work with consequent high gains and moderate decoding complexity (R. Haeb, "A Modified Trellis Coding Technique for Partial Response Channels," IEEE Transactions on Communications, Vol. 40, No. 3, pp. 513-520, March 1992).
While trellis coded modulation is recognized as a powerful coding technique, what is needed is a practical method and system for applying trellis coded modulation to general ISI channels.